The relaxed game chromatic number of outerplanar graphs

2004 ◽  
Vol 46 (1) ◽  
pp. 69-78 ◽  
Author(s):  
Charles Dunn ◽  
Hal A. Kierstead
Keyword(s):  
Chromatic Number ◽  
Outerplanar Graphs ◽  
Game Chromatic Number

scholarly journals Relaxed game chromatic number of trees and outerplanar graphs

2004 ◽  
Vol 281 (1-3) ◽  
pp. 209-219 ◽  
Author(s):  
Wenjie He ◽  
Jiaojiao Wu ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Outerplanar Graphs ◽  
Game Chromatic Number

scholarly journals The 6-relaxed game chromatic number of outerplanar graphs

2008 ◽  
Vol 308 (24) ◽  
pp. 5974-5980 ◽  
Author(s):  
Jiaojiao Wu ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Outerplanar Graphs ◽  
Game Chromatic Number

On the game chromatic number of splitting graphs of path and cycle

2019 ◽  
Vol 795 ◽  
pp. 50-56 ◽  
Author(s):  
Muhammad S. Akhtar ◽  
Usman Ali ◽  
Ghulam Abbas ◽  
Mutahira Batool
Keyword(s):  
Chromatic Number ◽  
Game Chromatic Number

scholarly journals The game chromatic number of random graphs

2008 ◽  
Vol 32 (2) ◽  
pp. 223-235 ◽  
Author(s):  
Tom Bohman ◽  
Alan Frieze ◽  
Benny Sudakov
Keyword(s):  
Chromatic Number ◽  
Random Graphs ◽  
Game Chromatic Number

scholarly journals Game Chromatic Number of Some Regular Graphs

2019 ◽  
Vol 09 (04) ◽  
pp. 159-164 ◽  
Author(s):  
Ramy Shaheen ◽  
Ziad Kanaya ◽  
Khaled Alshehada
Keyword(s):  
Chromatic Number ◽  
Regular Graphs ◽  
Game Chromatic Number

scholarly journals Strong Oriented Chromatic Number of Planar Graphs without Short Cycles

2008 ◽  
Vol Vol. 10 no. 1 ◽  
Author(s):  
Mickael Montassier ◽  
Pascal Ochem ◽  
Alexandre Pinlou
Keyword(s):  
Abelian Group ◽  
Chromatic Number ◽  
Planar Graphs ◽  
Oriented Graph ◽  
Minimal Order ◽  
Outerplanar Graphs ◽  
International Audience

International audience Let M be an additive abelian group. An M-strong-oriented coloring of an oriented graph G is a mapping f from V(G) to M such that f(u) <> j(v) whenever uv is an arc in G and f(v)−f(u) <> −(f(t)−f(z)) whenever uv and zt are two arcs in G. The strong oriented chromatic number of an oriented graph is the minimal order of a group M such that G has an M-strong-oriented coloring. This notion was introduced by Nesetril and Raspaud [Ann. Inst. Fourier, 49(3):1037-1056, 1999]. We prove that the strong oriented chromatic number of oriented planar graphs without cycles of lengths 4 to 12 (resp. 4 or 6) is at most 7 (resp. 19). Moreover, for all i ≥ 4, we construct outerplanar graphs without cycles of lengths 4 to i whose oriented chromatic number is 7.

scholarly journals Enumeration and Asymptotic Properties of Unlabeled Outerplanar Graphs

10.37236/984 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Manuel Bodirsky ◽  
Éric Fusy ◽  
Mihyun Kang ◽  
Stefan Vigerske
Keyword(s):  
Chromatic Number ◽  
Polynomial Time ◽  
Asymptotic Properties ◽  
Statistical Properties ◽  
Cycle Index ◽  
Outerplanar Graphs ◽  
Analytic Combinatorics ◽  
Exact Number ◽  
Asymptotic Number

We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number $g_{n}$ of unlabeled outerplanar graphs on $n$ vertices can be computed in polynomial time, and $g_{n}$ is asymptotically $g\, n^{-5/2}\rho^{-n}$, where $g\approx0.00909941$ and $\rho^{-1}\approx7.50360$ can be approximated. Using our enumerative results we investigate several statistical properties of random unlabeled outerplanar graphs on $n$ vertices, for instance concerning connectedness, the chromatic number, and the number of edges. To obtain the results we combine classical cycle index enumeration with recent results from analytic combinatorics.

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